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A study has been made of the X-band esr behaviour of a number of dilute alloys and intermetallic compounds containing s-state ions between 300K and 1.7K. A large negative g-shift has been observed in the most dilute alloys of Gd in Pd (to 1.77); the g-shift reducing at higher concentrations of Gd as the Pd d-band is filled. A positive g-shift has been observed in the Pd-Mn (to 2.15) and LaAl₂-Gd systems. The sign of the g-shifts has been related to theory. The temperature dependence of the g-value and linewidth in Pd-Gd and Pd-Mn alloys has been interpreted in terms of the effect of the increase in demagnetising fields in the particles of the sample at the onset of ferromagnetic order. The esr measurements in Pd-Mn show a form consistent with an increasing magnetisation in a field of 3KGauss at concentrations above 3at% Eh, in contrast to the results of static susceptibility measurements. Comparison of the present results with previous data suggests that in these dilute alloys there may be a frequency dependent contribution to the residual linewidth. The g-value and temperature dependence of the linewidth has been measured for a number of compounds. Characteristic forms of behaviour have been distinguished for ferromaenets (including GdA1₂, GdPt₂, GdCu₆, EuPd₂, EuPd and Pd₂MnSn) and antiferromagnets (including GdAg₃, GdCu₂, GdB₆, GdB₄, GdZn₁₂, Gd₂Zn₁7 and "GdCu₄"). In the last five antiferromagnets an increase in linewidth at temperatures far above the Neel point has been observed and tentatively interpreted in terms of an extended regime of short-range order. For a number of the compoundsl ordering temperatures have been predicted from the esr results. The compound GdPd₃ showed anomalous behaviour possibly characteristic of metamagnetism. Compounds of Lh in Zn showed completely anomalous esr behaviour.